Evaluate the derivative of f(x) at x = 1. I'll use the limit definition:
[tex]\displaystyle \lim_{x\to1} \frac{f(x)-f(1)}{x-1} = \lim_{x\to1} \frac{6x^2-x^3-5}{x-1} = \lim_{x\to1}(-x^2+5x+5) = 9[/tex]
Then using the point-slope formula, the equation of the tangent line to f(x) at the point (1, 5) is
y - 5 = 9 (x - 1)
y = 9x - 4
The equation of "tangent-line" to the curve "y = 6x² - x³" at the point (1, 5) is : y = 9x - 4.
To find the derivative of the function f(x) = 6x² - x³, we differentiate each term with respect to x:
f(x) = 6x² - x³,
f'(x) = d/dx (6x²) - d/dx (x³),
f'(x) = 12x - 3x²,
Now, we need to find f'(1), which means evaluating derivative at x = 1;
f'(1) = 12(1) - 3(1)²,
f'(1) = 12 - 3,
f'(1) = 9,
The slope of tangent-line at point (1, 5) is given by f'(1), which is 9;
Using the point-slope form of equation of line (y - y₁ = m(x - x₁)), where m = slope and (x₁, y₁) is the given point (1, 5);
⇒ y - 5 = 9(x - 1),
Simplify the equation:
⇒ y - 5 = 9x - 9,
⇒ y = 9x - 4,
Therefore, the required equation of tangent-line is y = 9x - 4.
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Explain why rational numbers are "friendly."
Answer:
What makes a number friendly?
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same "abundancy" form a friendly pair; n numbers with the same "abundancy" form a friendly n-tuple.
Step-by-step explanation:
Please answer this math riddle for me ASAP!!! please
I am a four-digit number. My first number has no use because the number would be the same without it. My second and third numbers are mirror images and my fourth number is half of my second number.
Answer:
0884
Step-by-step explanation:
विपरीत अर्थवाले शब्द लिखिए ।
1. नदी २. इच्छा ३. आशा ४. अपकार
Answer:
sorry I can't understand the word
The zero of F -1(x) in F(x) = x + 3 is
-3
0
3
Answer:
The only zero of [tex]F^{-1}(x)[/tex] is [tex]3[/tex].
Step-by-step explanation:
The function [tex]F^{-1}[/tex] is the inverse of function [tex]F[/tex].
For a given [tex]x[/tex] and a given [tex]y[/tex], [tex]F^{-1}(y) = x[/tex] if and only if [tex]F(x) = y[/tex].
Let [tex]y[/tex] be a zero of [tex]F^{-1}(y)[/tex]. That is, [tex]F^{-1}(y) = 0[/tex].
By the reasoning above, since [tex]x = 0[/tex] and this particular [tex]y[/tex] satisfy [tex]F^{-1}(y) = x[/tex], it must be true that [tex]F(x) = y[/tex] for the same [tex]x = 0\![/tex] and [tex]y\![/tex].
Since [tex]x = 0[/tex] and [tex]F(x) = x + 3[/tex], [tex]F(0) = 3[/tex]. Therefore, [tex]y = F(0) = 3[/tex] since [tex]y = F(x)[/tex].
Thus, the zero of [tex]F^{-1}(y)[/tex] would be [tex]y = 3[/tex].
write the simplest polynomial function with the given zeros 2 √2, √5 and -3
Answer:
A. P(x) = x⁵ + 3x⁴ - 13x³ - 39x² + 40x + 120Step-by-step explanation:
With the given zero's, the polynomial is:
P(x) = (x - 2√2)(x - √5)(x + 3)Open parenthesis in steps:
1. (x - 2√2)(x - √5) = x² - (2√2 + √5)x + 2√10 = x² - 2x√2 - x√5 + 2√10
2. (x² - 2x√2 - x√5 + 2√10)(x + 3) =
x³ - 2√2x² - √5x² + 2√10x + 3x² - 6√2x - 3√5x + 6√10 =
x³ + 3x² - 2x²√2 - x²√5 - 6x√2 - 3x√5 + 2x√10 + 6√10
This is not matching any options so we add two more zero's: -2√2 and -√5
New polynomial looks like:
P(x) = (x - 2√2) (x + 2√2)( x - √5)(x - √5)(x + 3)Open parenthesis in steps:
1. (x - 2√2) (x + 2√2) = x² - 82. (x - √5) (x + √5) = x² - 53. (x² - 8)(x² - 5) = x⁴ - 8x² - 5x² + 40 = x⁴ - 13x² + 404. (x⁴ - 13x² + 40)(x + 3) = x⁵ + 3x⁴ - 13x³ - 39x² + 40x + 120P(x) = x⁵ + 3x⁴ - 13x³ - 39x² + 40x + 120What is 449,650 rounded to the nearest ten thousand?
400,000
440,000
449,000
450,000
Answer:
450,000
Step-by-step explanation:
The ten thousand digit is 4 and if we compare it to 9, it is bigger then 5 therefore it is rounded up and you get the answer of 450,000
Simplify The following completely:
[tex]\sqrt{48}[/tex]
Answer:
4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
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Given : Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’s bill is 7%.
To Find : How much is Isaac’s total bill?
b) 25% discount off before tax
Solution:
one pair for $37.00
second pair for $42.00
Total Bill before taxes = 37 + 42 = 79 $
7 % Sale Tax = (7/100)79 = 5.53 $
Isaac’s total bill = 79 + 5.53 = 84.53 $
Total Bill before taxes = 37 + 42 = 79 $
Discount 25 % = (25/100)79 = 19.75$
Total Bill before taxes = 79 - 19.75 = 59.25 $
7 % Sale Tax = (7/100)59.25 =4.1475 $
Isaac’s total bill = 59.25 + 4.1475 = 63.3975 $
Please post Question one by one
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Answer fast, please!!
The hypotenuse of a right triangle is 15 cm. One of the triangles legs is two times the length of the other leg
Step-by-step explanation:
to solve you will use the formula c2=a2+b2 where c2 is always the hypotenuse and a2 and b2 are the rest of the sides. So c2 will be (15)2 and a2 will be (2x)2 while b2 will be represented by x2.Calculate (15)2=(2x)2+x2 You will get 225=4x2+x24x2+x2 will give you 5x2Then you will divide 225 by 5x2 and find the square root of it.√45 is an irritational number since it has no perfect square so you will use the long division method.Your answer will be 6.708what is the quotient of 2x+5/4 ÷ 2x+5/6
a. 1/4
b. 1/2
c. 2/3
d. 3/2
I will gladly give brainliest.
4 ( 2x - 3) -2 ( x + 1)
Answer:
6x - 14
Step-by-step explanation:
4(2x - 3) - 2(x + 1)
1. Expand both brackets
(8x - 12) - (2x + 2)
2. Simplify
8x - 2x = 6x
-12 - 2 = -14
Therefore, 4(2x - 3) - 2(x + 1) = 6x - 14
how to multiply 21 x 25 in oldschool way
I dont understand Analyze and solve percent problems
Answer:
okay, well, is there any link u wanna post for us to help u? maybe we can explain it?
Step-by-step explanation:
what are some expressions to solve a product of 120? a(6x10)+(20x10) b.20x6 c. (6x2)+(10x2) d.(2x5)+(55x2)
Answer: D. i took the test.. Happy to Help! :)
Step-by-step explanation:
a line that is parallel to y=-3x+2 and contains the point (3,-3)
Answer:
y = -3x + 6
Step-by-step explanation:
Two lines that are parallel will have the same slope. All we need to do is find the new y-intercept.
-3 = -3(3) + b
-3 = -9 + b
6 = b
Now we can input the stuff we know and solved for back into the original formula [ y = mx + b ].
y = -3x + 6
Best of Luck!
A parallel line means our new line will have a slope equal to the original line.
The original line is in slope-intercept form, y = mx + b, where m is the slope and b is the value of the y-intercept. This tells us that the slope we want to use is m = -3
By using a slope of -3, with the given point (3,-4), we can now use the point-slope formula to find our new line.
Point-slope formula: y - y1 = m(x - x1) where m is the slope and the line passes through the point (x1,y1)
Combining our point and slope, we get:
y + 4 = -3(x - 3)
If we wish, we can rearrange this by distributing on the right hand side.
y + 4 = -3x + 9
We can then subtract 4 from both sides to get our answer in slope-intercept form
y + 4 - 4 = -3x + 9 - 4
y = -3x + 5
A plumber charges 1/4 of the cost of materials as a labor fee. If the materials for the current job cost $130.00, how much will the plumber charge the client?
Answer:32.5
Step-by-step explanation: i used a calculator
Answer:
$162.50
Step-by-step explanation:
wich one is bigger 4\5 or 0.8
Answer: They both equal the same thing.
Step-by-step explanation: 4/5=0.8
Answer: there both equal
Step-by-step explanation:
4/5 is basically 0.8 cuz 0.8 put a extra 0 in it its gonna say 0.80 and 4 x 20= 80. and that's 80/100 so yea..... 4/5 and 0.8 are equal.
this my first time answering. Sorry if I get it wrong TwT
After extensive measurements of the time necessary to complete the first homework assignment, a teacher determines that there is a population mean of 100 and a standard deviation of 20. If she samples a class of 60 students and calculates a mean of 96 minutes, what is the z statistic
Answer: The guideline doesn’t account for students who may need to spend more—or less—time on assignments. In class, teachers can make adjustments to support struggling students, but at home, an assignment that takes one student 30 minutes to complete may take another twice as much time—often for reasons beyond their control.
Step-by-step explanation:
Hope this helps!
elect the correct answer from each drop-down menu.
Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a
.
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a
.
Answer:
1. Triangle XYZ undergoes a translation.
2. Triangle X'Y'Z' undergoes a reflection across the x-axis
answer this question for a brainly
Answer:
The missing value is 56.
Step-by-step explanation:
All side angles must add up to 180. So given the 2 angle measures 30+94 = 124.
Then subtract 180 from 124 to get your answer of 56.
When you add up all the angles, it gets you 180 evenly.
The principal of a school is hosting a small luncheon for her staff. She plans to prepare two sandwiches for each person. Some staff members offer to bring salads and beverages.
The principal has a budget of $225 and expects at least 16 people to attend. Sandwiches cost $3 each.
Select all of the equations and inequalities that could represent the constraints in the situation, where n is the number of people attending and s is the number of sandwiches.
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Select all that apply:
A. n ≥ 16
B. n ≥ 32
C. s < 32
D. s = 2n
E. 3n ≤ 225
F. 3s ≤ 225
The constraints in the question are given by the definition of the variables;
The constraints are represented by the following equation and inequalities.
A. n ≥ 16D. s = 2·nF. 3s ≤ 225Reasons:
The budget of the principal = $225
Number of people expected = 16 people
Number of sandwich per person = 2
Cost of each sandwich = $3
Required:
To select the inequalities that represent the situation's constraint
Solution:
The variable that represent the number of people attending = n
The number of sandwiches = s
From the question , we have;
The number of sandwich per attendee = 2 sandwiches
The total number of sandwich, s, for n attendees = 2·n
Therefore, we have;
s = 2·n
The number of people attending is at least 16, therefore;
n ≥ 16
The cost of the s sandwich = $3 × s
The total cost should be less than or equal to given budget of $225,
therefore;
3s ≤ 225
The equations and inequalities that could represent the constraints are;
A. n ≥ 16, D. s = 2·n, and F. 3s ≤ 225
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QUIZ:
Add Signed Decimals
Add.
-2.34 + (-1.052)
Enter your answer in the box.
Answer:
-3.392
Step-by-step explanation:
Math-way
कौन-सा शब्द यौगिक है।
क. पुस्तकालय। ख. भाई की बहन। ग लंकेश
Answer:
help please............
I need help please hurry<343
Answer:
42 inches
Step-by-step explanation:
1. To convert feet into inches, multiply the # of feet by 12.
[tex]3\frac{1}{2}*12[/tex] [tex]\frac{7}{2} *12[/tex] [tex]\frac{84}{2}[/tex] [tex]42[/tex]Therefore, 3 1/2 feet in inches is 42 inches.
Answer:
42 inches
Step-by-step explanation:
3.5 feet x 12 inches = 42 inches
direct variation
Hooke's Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. if a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?
pls help (;ŏ﹏ŏ)
When a force of 270N is applied, the spring stretch by 7.5cm
Two variables are said to be directly proportional if as one variable increases/decreases, the other variables does the same by the same amount.
Let F represent the force and x represent the extension, hence:
F ∝ x
F = kx; k is the constant of proportionality
When F = 180, x = 5, hence:
180 = 5k
k = 36
F = 36x
When F = 270:
270 = 36x
x = 7.5 cm
When a force of 270N is applied, the spring stretch by 7.5cm
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Help Please, Missing Geometry Class because I am sick and don't understand this.
Answer:
niether do i
Step-by-step explanation:
Select the correct answer. What is a round character? A. a character who contrasts the personality of another character B. a character who stays the same throughout a story C. a character who has a complex personality D. a character who has just one or two personality traits
what is the sum of 1/6 and 5/12
Answer:
7/12
1/6 to 2/12 add 5/12 to get 7/12
Nyashid
Solving n/3 - 1 = 8
N/3-1 = 8 in the
Click New. You should now see the equation
Gizmo.
Step One: This equation has two operations, division an
subtraction. Which operation should you undo first?
Choose (drag) the correct step in the
Gizmo
Step Two: What operation should you undo next?
Choose (drag) the correct step in the Gizmo.
Stop & Check: Substitute your solution for n in the equation and
evaluate. Does your solution produce a true statement? If so, your
answer is correct!
TolutionWhat is the solution to n/3-1 = 8?
Step-by-step explanation:
first you need to tranfer 1 to RHS do the addition
n/3 = 8+1
=) n/3 = 9
then you need to transfer 3 to RHS and multiply
=> n = 9 x 3
there for n = 27